We adopt an atomistic pseudopotential description of the electronic structure of self-assembled, lens-shaped InAs quantum dots within the ''linear combination of bulk bands'' method. We present a detailed comparison with experiment, including quantites such as the single-particle electron and hole energy level spacings, the excitonic band gap, the electron-electron, hole-hole, and electron-hole Coulomb energies and the optical polarization anisotropy. We find a generally good agreement, which is improved even further for a dot composition where some Ga has diffused into the dots.

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